On Monday, nearly 100,000 call attempts were made by 10 a.m., when the call center normally receives 6,000 calls in an entire week. The department put in place a new process under which those filing claims submit their forms at specified times based on their last names. Even so, Ms. Haavind said, the crush of applications has strained not just the department’s systems but also its employees.

“They are talking to stressed-out people, and they are also stressed out,” she said.

For laid-off workers, the anxiety is racking.

Mere weeks ago, Bill Copperfield had steady work installing drywall in commercial buildings in Hawaii. Then he caught a cold and, in the suddenly cautious world of coronavirus, was told not to come to work, meaning he wasn’t paid. By the time he was healthy again, the job had shut down and the state government was telling nonessential workers to stay home. He has tried repeatedly to file an unemployment claim, but hasn’t managed to get through.

“So right now I am three weeks without income and I’ve got my rent coming up, I’ve got food I’ve got to buy,” Mr. Copperfield said. “Definitely I won’t be paying bills this month.”

Mr. Copperfield, 45, has been laid off in the past, including during the 2008-2009 housing crisis, in which he ended up losing his home to foreclosure. But even then, he said, he was able to go out and find work as a handyman or even sell fish he caught.

“At least then I could go out and hustle work, even if it wasn’t in my field,” he said. “Nobody can work right now, we’re on like lockdown. And even if I could find side work, I’d be putting my family at risk.”